Answer:
Dog hear better than people. Hearing dogs are most used in a home setting, but with extra training can work in public. The dogs are trained to listen for certain sounds and to signal their handler, usually by touch.
When the dog hears the doorbell, it will touch the handler and go to the door. If the handler doesn't follow, it will again go touch the handler and lead them to the door.
Other sounds that are trained are baby cry, oven and microwave timers, alarm clocks and phone ringing.
An example is a deaf couple. Both had their own dog. Each dog was trained on one specific alarm clock. So in the morning only the correct person was woken up, the dogs usually paw the chest or lay on you to wake you up.
The smoke/fire alarm is a special sound. You don't want the dog leading a handler to a fire, since that is where the alarm is at. Our dogs are trained to lay on the floor and rub their nose to indicate smoke so the handler can choose how to get out safely.
When in a public setting, out for a walk or in a restaurant the dog acts as another pair of ears. The handler can look at the dogs head and ears and see where sounds are coming from, our dogs are trained to sit and silent howl when a siren is near, alerting the deaf handler not to walk in a street until they are sure it's safe.
Contrary to belief, hearing dogs are NOT trained to bark, as barking is rude in public.